Hard as it is to believe now, there was a time when making a black comedy about Stalin's tyrannical rule and The Great Terror, would've have been considered to be in questionable taste. Precisely, that time was 1983, when the fledgling Channel 4 broadcast Red Monarch, a dark farce about Stalin's reign, which was received with some criticism in the press (almost certainly the Daily Mail, it's always the Daily Mail) for trivializing such horror. These days of course, ghoulish black comedy is our default setting; the way we get through the day.

Armando Iannucci's sweary political satire, The Thick Of It, originally conceived as a modern-day version of Yes, Minister, has become like one of those game show formats that can be franchised off all over the world. So far, Iannucci has chosen to oversee its spread himself (applying it just to the American market in Veep by way of the film In The Loop) but you could easily imagine a version for every nation, just like The Weakest Link.

Now he has moved it into the realms of costume drama with this version of Stalin's final day, adapted from a French graphic novel. In its telling of the squabble for power afterward between Khrushchev (Buscemi) and the head of NKVD secret police Beria (Beale), it is in many ways a remake of The Thick Of It special The Rise Of The Nutters. The fawning, duplicity and cynicism of the political game are the same, but here it has a body count.

Retrofitting it to the USSR has required some tinkering with the formula. The absurdities are pushed a bit further and while previous Iannucci's satires went on inside Westminster/ Washington bubbles, here the brutal consequences – executions, roundups, rapes - happen on screen. As soon as the main players have moved off, armed forces will sweep in to massacre the extras.

The film is genuinely funny and casually chilling. Palin's performance as Molotov captures a man so blindly loyal to the cause he wouldn't accept his ideals had been corrupted even if it was putting a bullet in his head. It's reminiscent of his turn in Brazil: he's great at playing deluded submissives. The cast is wild mixtures of people who have no place being in a film together, and the film plays on the absurdity of this collection by having them play their roles in a variety of accents.

The film is absurd, but credibly absurd. Its depiction of life in the heart of a totalitarian tyranny, with its ludicrous levels of paranoia, feels believable. Buscemi's Khrushchev (who looks oddly similar to Adlai Stevenson) goes home after a night with Stalin and dictates to his wife everything he said to the leader, and the leader's response to everything he said, so he can work on the bits that went well. Surprisingly Beria, a man who used his power to force himself on any woman he could and was almost whimsical in his killing and torturing, is presented quite ambiguously.It is hinted he might have gone on to become a genuine reformer.

The movie cements Iannucci's position as the foremost satirist of his age, unless Chris Morris feels inclined to make a fight of it. I wonder though what we have really gained from his work, all these self-fulfilling parodies. His portrait of our insular political classes as shallow, lazy and completely removed from reality only seems to have given them license to be shallower, lazier and even more removed from reality. From Chaplin onwards, history demonstrates that showing up tyrants as buffoons doesn't put the slightest dent in their appeal. Indeed, clown face is how all tyranny now presents itself, coming at us with clown hair, clown bluster and clown children's names as they make their name on Letterman or Have I Got News For You.